18.2.2 Improved Data Gathering and Processing
The system that generated the curves for a specific room in Figure 18.5 was an important beginning, but improvements were possible. What was missing was a statistical perspective on many rooms, so we might develop a similar kind of measure that suggested performance in a "typical" room.
Figure 18.6 describes the data-gathering system at Harman International, Northridge, California. It incorporates a computer-controlled rotating platform upon which the loudspeaker is placed on its bottom to measure the horizontal orbit at 10° intervals and then on its side to measure the vertical orbit. The height of the platform is adjusted to bring the reference axis to the same point. The data for the 70 frequency response curves have a frequency resolution of 2 Hz, the curves are 1/20-octave smoothed, and the anechoic chamber is anechoic (±0.5 dB, 1/20-octave) from 60 Hz to beyond 20 kHz and has been calibrated to be accurate (±0.5 dB, 1/10-octave) from 20 to 60 Hz (Devantier, 2002). The vertical scale has been adjusted to show the sound level corrected to the standard 1 m distance so sensitivity can be read directly.
FIGURE 18.6 The data collecting system used at Harman International and the basic set of processed data that it yields.
The family of curves shown in the lower half of the figure is the set of data calculated to describe sounds that might arrive at a listener's ears in an average room. All of the data are based on the selection of a reference axis, the axis along which the on-axis curve is measured. Normally this has a point of origin between the tweeter and midrange drivers, and it extends perpendicularly outward from the front baffle. It is possible for a manufacturer to specify any axis as its reference, but logically it would be the line that, if extended into the listening room, would come close to a seated listener's ears. These are the curves:
• The on-axis frequency response is the universal starting point, and in many situations it is a fair representation of the first sound to arrive. However, as shown in the Devantier (2002) survey, over half of those investigated had the prime listening position 10° to 20° off axis. Hence, a justification for the following measure.
• The listening window is a spatial average of the nine frequency responses in the ±10° vertical and ±30° horizontal angular range. This embraces those listeners who sit within a typical home theater audience, as well as those who disregard the normal rules when listening alone. Because it is a spatial average, this curve attenuates small fluctuations caused by acoustical interference, something far more offensive to the eye than to the ear, and reveals evidence of resonances, something the ear is very sensitive to: interference effects change with microphone position and are attenuated by the spatial averaging, whereas resonances tend to radiate similarly over large angular ranges and remain after averaging. Bumps in spatially averaged curves tend to be caused by resonances.
• The early reflections curve is an estimate of all single-bounce, first reflections in a typical listening room. Measurements were made of early reflection "rays" in 15 domestic listening rooms. From these data, a formula was developed for combining selected data from the 70 measurements to develop an estimate of the first reflections arriving at the listening location in an "average" room (Devantier, 2002). It is the average of the following:
- Floor bounce: average of 20°, 30°, 40° down
- Ceiling bounce: average of 40°, 50°, 60° up
- Front wall bounce: average of 0°, ±10°, ±20°, ±30° horizontal
- Side wall bounces: average of ±40°, ±50°, ±60°, ±70°, ±80° horizontal
- Rear wall bounces: average of 180°, ±90° horizontal
The number of "averages" mentioned in that description may make it seem as though anything useful would be lost in statistics. However, this turns out to be a very useful metric. Being a substantial spatial average, a bump that appears in this curve, and in other curves is clear evidence of a resonance. It is also, as will be seen, the basis for a good prediction of what is measured in rooms.
• Sound power is intended to represent all the sounds arriving at the listening position. It is the weighted average of all 70 measurements, with individual measurements weighted according to the portion of the spherical surface that they represent. Sound power is a measure of the total acoustical energy radiating through an imaginary spherical surface with the radius equal to the measurement distance. Thus, the on-axis curve has very low weighting because it is in the middle of other, closely adjacent measurement points (see the perspective sketch at the top of the figure), and measurements further off axis have higher weighting because of the larger surface area that is represented by each of those measurements. Ideally, such a measurement would be made at equally spaced points on the entire surface of the sphere, but this simplified spatial-sampling process turns out to be a very good approximation. The result could be expressed in acoustic watts, the true measure of sound power, but here it is left as a sound level, a frequency response curve having the same shape. This serves the present purposes more directly. Any bump that shows up in the other curves and persists through to this ultimate spatial average is a noteworthy resonance.
• Directivity index (DI) is defined as the difference between the on-axis curve and the sound-power curve. It is thus a measure of the degree of forward bias - directivity - in the sound radiated by the loudspeaker. It was decided to depart from this convention because it is often found that because of symmetry in the layout of transducers on baffles, the on-axis frequency response contains acoustical interference artifacts, due to diffraction, that do not appear in any other measurement. It seems fundamentally wrong to burden the directivity index with irregularities that can have no consequential effects in real listening circumstances. Therefore, the DI has been redefined as the difference between the listening window curve and the sound power. In most loudspeakers, the effect of this choice is negligible, but in highly directional systems it is significant because the listening window curve is lower than the on-axis curve. In any event, for the curious, the raw evidence is there to inspect. Obviously, a DI of 0 dB indicates omnidirectional radiation. The larger the DI, the more directional the loudspeaker in the direction of the reference axis.
FIGURE 18.7 An examination of different forms of misbehavior, as revealed in the family of frequency-response curves.